Transient time-domain resonances and the time scale for tunneling

Abstract

Transient time-domain resonances found recently in time-dependent solutions to Schrodinger's equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time-frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to nontunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum t(max) of the time-domain resonance corresponds to under-the-barrier tunneling. We argue that t(max) represents the relevant tunneling time scale through the classically forbidden region.